The communication complexity of a function f(x, y) measures the number of bits that two players, one who knows x and the other who knows y, must exchange to determine the value f(x, y). Communication complexity is a fundamental measure of complexity of functions. Lower bounds on this measure lead to lower bounds on many other measures of computational complexity. This monograph survey lower bou...

Choosing a language for knowledge representation and reasoning involves a trade-off between two competing desiderata: succinctness (the encoding should be small) and tractability (the language should support efficient reasoning algorithms). The area of knowledge compilation is devoted to the systematic study of representation languages along these two dimensions—in particular, it aims to determ...

Suppose each of k ≤ no(1) players holds an n-bit number xi in its hand. The players wish to determine if ∑ i≤k xi = s. We give a public-coin protocol with error 1% and communication O(k lg k). The communication bound is independent of n, and for k ≥ 3 improves on the O(k lg n) bound by Nisan (Bolyai Soc. Math. Studies; 1993). Our protocol also applies to addition modulo m. In this case we give ...

A more sophisticated understanding of the unpredictable, disorderly and unstable aspects of healthcare organisations is developing in the knowledge translation (KT) literature. In an article published in this journal, Kitson et al introduced a new model for KT in healthcare based on complexity theory. The Knowledge Translation Complexity Network Model (KTCNM) provides a fresh perspective by mak...

We prove n lower bounds on the multiparty communication complexity of AC functions in the number-on-forehead (NOF) model for up to Θ(logn) players. These are the first lower bounds for any AC function for ω(log logn) players. In particular we show that there are families of depth 3 read-once AC formulas having k-player randomized multiparty NOF communication complexity n/2. We show similar lowe...

PH cc ⊆ BP · ⊕P cc ⊆ PSPACE cc .

A well-studied class of functions in communication complexity are composed functions of the form (f ◦ g)(x, y) = f(g(x, y), . . . , g(x, y)). This is a rich family of functions which encompasses many of the important examples in the literature. It is thus of great interest to understand what properties of f and g affect the communication complexity of (f ◦ g), and in what way. Recently, Shersto...